In principal, differential current protection compares measured currents from the ends of an electric line regarding both the magnitude and the phase angle. In operation, there must be an interconnecting channel between the line end relays, over which the interchange of current information is transferred. According to Kirchhoff's law, when the vector sum of these currents differs from zero, it indicates a fault in the protected line. Such differential current protection is the simplest form of line protection requiring only few settings to be entered regarding the characteristic of the protected line.
It is known that line differential current protection has been implemented according to the phase segregated or the combined sequence principle. In the phase segregated scheme, differential current protective functions are implemented on per phase-current basis. The phase current differential computations determine whether a fault has occurred and identify which phase or phases is/are involved in the fault. In the combined sequence scheme, in order to reduce the communication capacity requirements while maintaining adequate operation speed and reliability of operation, only one single signal instead of all three phase currents are interchanged between the line ends. This signal is a proper combination of the line positive-sequence, negative-sequence and zero-sequence currents. The differential current computations are then based on this combined sequence current signal.
The basic principle of the phase segregated scheme is that the differential (operate) quantity in the current differential function is the magnitude of the phasor summation of the local and remote phase currents. Thus, the operate quantity is equal to the total fault currents for internal faults and equal to zero (neglecting line distributed capacitance charging currents) for external faults. For phase A it can be written:IOPphA=|ĪLphA+ĪRphA|  (eq01)
The scheme must be restrained so that certain level of apparent operate current resulting from, for example, CT and other measuring errors that are proportional to the magnitude of the measured phase currents can be allowed without the risk of false operation. The restraint (stabilizing) current for phase A can be calculated, for example, as:
                              I          RESphA                =                                                                                            I                  _                                LphA                                                    +                                                                          I                  _                                RphA                                                            2                                    (        eq02        )            
where
ĪLphA is the local end phasor representing phase current, A and
ĪRphA is the remote end phasor representing phase current A
Equations 01 and 02 assume positive current flow from the busbar towards the line in both line ends. Similar equations apply for phases B and C.
The scheme can also be based on the combined sequence current, which is a weighted sum of phase A symmetrical component currents. Let ĪT represent this combined current, and let C1, C2 and C0 represent the weighting coefficients for positive-, negative-, and zero-sequence components, then ĪT can be described as:ĪT=C1Ī1+C2Ī2+C0Ī0   (eq03)
where Ī1, Ī2 and Ī0 represent phase A positive-sequence, negative-sequence, and zero-sequence currents, respectively.
For the combined sequence scheme, the operate and restraint currents can be written in a way similar to the above:
                              I                      T            OP                          =                                                                      I                _                                            T                L                                      +                                          I                _                                            T                R                                                                                  (        eq04        )                                          I                      T            RES                          =                                                                                            I                  _                                                  T                  L                                                                    +                                                                          I                  _                                                  T                  R                                                                            2                                    (        eq05        )            
where
ĪTL is the local end phasor representing the combined sequence current, and
ĪTR is the remote end phasor representing the combined sequence current.
The operating principle of the traditional solutions in the simplest form is given by the equation:IOP>k·IRES+IB   (eq06)
where
IOP is the calculated operate current,
IRES is the calculated restraint current,
k is the characteristic slope setting, and
IB is the basic start current threshold setting.
The operating criterion states that the higher the restraint current is, the higher operate current threshold is required to operate the relay. The correspondence between these two current quantities is given by the slope setting k.
In general, the limit of sensitivity of the traditional schemes is basically dictated by the amplitude of the charging current of the protected line. This charging current is due to the distributed capacitance (phase-to-phase and phase-to-earth capacitance) of the protected line and is seen as apparent differential current by the relay. As a general rule, the setting of the differential current protection is such that it overrides the effect of the charging current. To mitigate this problem, some manufacturers have introduced a so-called charging current compensation function to somewhat increase the sensitivity of the protection. This feature can be used with phase segregated schemes and it is known by various relay manufacturers. Examples are given in documents: Siemens A G, “SIPROTEC, Line Differential Protection with Distance Protection 7SD52/53, V 4.60, Manual”, and ABB AB Substation Automation Products, SE-721 59 Västerås, Sweden, “Application manual Line differential protection IED RED 670”, December 2007. The main purpose of the charging current compensation function is to enable adequately sensitive differential current protection of long transmission lines and cables in low-impedance or solidly earthed networks, where otherwise the magnitude of the charging current would require increasing of the basic start current threshold setting of the traditional schemes too much. The magnitude of the charging current is directly proportional to the system voltage level and to the magnitude of the distributed capacitance of the protected line.
In the combined sequence schemes, the sensitivity is additionally affected by the choice of the weighting coefficients. Increasing of weighting coefficient C2 (eq03) can increase the earth fault sensitivity and reduce the sensitivity difference between three-phase faults and earth faults in cases where the earth fault current is lower than the three-phase fault current. In order to increase the sensitivity of earth faults and at the same time to keep the sensitivity of phase faults unaffected, a non-zero weighting coefficient C0 (eq03) can be used.
As a general rule, the maximum sensitivity that can be achieved by the above schemes depends on the setting of the basic start current threshold level as follows:
No charging current compensation feature in use:                IB≧2.5*ICHARGE         
Charging current compensation feature in use:                IB≧1.0*ICHARGE         
where ICHARGE is the corresponding charge current component of the protected line calculated according to its positive-, (negative-) or zero-sequence capacitance depending on the applied scheme.
The fundamental problem of the above schemes when considering their application in unearthed and compensated networks is that in order to ensure adequate sensitivity, the basic start current threshold setting level would have to be set well below the charging current of the protected line, and this cannot be done with the above schemes. It can be said that for that reason these schemes are not able to detect earth faults, at least not when fault resistance becomes involved in the fault.
Therefore, the sensitivity of such traditional solutions is typically adequate only against short circuit faults and against earth faults in low-impedance and solidly earthed networks, where the magnitude of earth fault current is typically always higher than 25% of the three-phase short circuit current. Considering earth faults in high-impedance earthed and unearthed networks, the magnitude of earth fault current can be as low as a few amperes. It is therefore evident that the traditional solutions cannot be used for earth fault protection in such networks. However, selective earth fault protection is also required for lines where line differential current protection is applied against short circuits. It would therefore be highly valuable to have a dedicated differential current protection function with high sensitivity against earth faults.
FIG. 1 shows known network arrangements where line differential current protection is applied as the main protection. As the network arrangements of FIG. 1 are highly meshed and may also contain distributed generation, the application of the line differential current protection is very well justified, but the fundamental problem is how to take care of the dedicated earth fault protection of these lines such that the operation is selective, sensitive and fast enough despite the changing network configurations due to daily operation.
JP 2002186165 describes a solution to provide a differential current relay which is fitted to an unearthed system with meshed distribution lines and which does not need synchronization among data collected at individual terminals. According to this solution, by determining the sign of the sum of imaginary parts Im[Ī0AV0A*], i.e. of the product of the zero-sequence current and the complex conjugate of the zero-sequence voltage, and Im[Ī0BV0B*] based on measurements from line ends A and B, respectively, it can be judged whether an earth fault occurs in the section between the differential current relay A and the neighboring differential relay B. A drawback of the described solution is that it can only be applied in unearthed networks.